Abstract

Image segmentation is an important topic in computer vision and image processing. As a region-based (global) approach, the Mumford and Shah (MS) model is a powerful and robust segmentation technique as compared to edge-based (local) methods. In this thesis we apply the MS model to two interesting problems: image inpainting and text line detection. We further extend it by proposing a new image segmentation model to overcome some of the difficulties of the original model. As a demonstration of the new model, we apply it to
the segmentation of retinal images. The results are better than the
state-of-the-art approaches.

In image inpainting, the MS model is used to detect and estimate the object boundaries inside the inpainting areas. These boundaries are preserved in the inpainting results. We present a hierarchical segmentation method to detect boundaries of both the main structure and the details. The inpainting result can preserve detailed edges.

In text line detection, we use a combination of Gaussian blurring, the MS model, and morphing method. Different from other general text image detection approaches, our method segments text documents without any knowledge of the written texts, so it can detect handwriting text lines of different languages. It can also handle different gaps and overlaps among the text lines.

Although the MS model has been used successfully in many applications, its implementation has always been based on some forms of approximation. These approximations are either inefficient computationally or applicable only to some special cases. Our new model consists of only one variable, the segmentation curve, therefore the computation is very efficient. Furthermore, no approximation is required, hence the method can segment objects with complicated intensity distribution. The new model can detect both step and roof edges, and can use different filters to detect objects of different levels of intensity. To show the advantages of the new model, we use a combination of the new model and Gabor filter to detect blood vessels in retinal images. This new model can detect objects with complicated image intensity distribution, and can handle non-uniform illumination cases effectively.